针对光谱重构领域中光谱数据量较大与重构精度较低的问题, 提出了一种光谱可调谐的光谱重构方法。 在此之前国内外相关研究均是在数百条膜系的基础上进行, 并且计算过程比较复杂, 该方法利用10条膜系针对不同的单色光源进行实验并进行光谱重构。 光谱重构数学模型可以用线性方程组 AX= B表示, 在实验过程中会受到多种误差源的干扰, 如膜系加工与设计间的误差、 探测器量子效率拟合误差、 杂散光干扰误差以及灰度值选取的误差等。 这些误差源造成了线性方程组变为病态方程, 造成了目标光谱信息解算的不准确。 在解算目标光谱信息的过程中, 首先在400~900 nm波长范围内利用凸优化算法解出含有误差的目标光谱信息的初始值, 并进行初次拟合, 得出含有误差的光谱曲线。 然后利用已知的光谱曲线信息判断目标光谱的有效波长范围, 对目标光谱范围进行伸缩, 在此范围内进行二次局部解算, 得出局部波长内的光谱信息, 然后对局部光谱信息进行局部拟合, 结合初次拟合结果, 得出新的目标光谱拟合曲线, 进一步提高了光谱重构精度, 以此类推, 得出精度较高的目标光谱曲线。 针对重构精度的评价指标不仅采用了国内外广泛使用的ARE, MSE与RQE, 还首次提出了一种新的评价光谱重构精度的指标, 即计算目标有效波长范围内每隔10 nm的MSE值, 若每10 nm的MSE值小于0.1, 则认为光谱重构精度达到了10 nm, 该方法不仅有效避免了在求解出现严重偏离真实值的情况, 还在凸优化解算过程中提供了约束条件, 有利于提高重构精度。 实验结果表明该方法在保证MSE, ARE与RQE高精度的条件下, 每隔10 nm的MSE最小值达到了0.002 3。 基于光谱可调谐光谱重构方法不仅达到了对目标光谱达到高精度重构的效果, 而且实现了数据降维。 此方法为光谱重构领域的工作方向提供了新的思路, 在工程上具有较大的应用价值。

Aiming at the problem of a large amount of spectral data and low reconstruction accuracy in the field of spectral reconstruction, a spectral tunable spectral reconstruction method is proposed. Prior to this, domestic and foreign-related research were carried out based on hundreds of film systems, and the calculation process was relatively complicated. This method uses 10 film systems to conduct experiments against different monochromatic light sources and perform the spectral reconstruction. Linear equations can express the mathematical model of spectral reconstruction. During the experiment, it will be interfered with by various error sources, such as the error between film processing and design, the fitting error of the detector quantum efficiency, the stray light interference error, the error of grey value selection, etc. These error sources cause the linear equations to become ill-conditioned equations, resulting in an inaccurate solution of the target spectrum information. In calculating the target spectral information, firstly, the convex optimization algorithm is used to solve the initial value of the target spectral information with errors in the wavelength range of 400~900 nm, and the initial fitting is performed to obtain the spectral curve with errors. Then use the known spectral curve information to determine the effective wavelength range of the target spectrum, expand and contract the target spectral range, perform a secondary local calculation in this range, and obtain the spectral information within the local wavelength. Then the local spectral information is locally fitted, combined with the initial fitting results, and a new target spectral fitting curve is obtained, which further improves the accuracy of the spectral reconstruction and obtains a higher-precision target spectral curve. The evaluation index for reconstruction accuracy not only adopts the widely used ARE, MSE and RQE at home and abroad but also proposes a new index for evaluating the accuracy of spectral reconstruction for the first time, which is to calculate the MSE value every 10 nm within the effective wavelength range of the target. If the MSE value per 10 nm is less than 0.1, the spectrum reconstruction accuracy is considered to have reached 10 nm. This method effectively avoids the serious deviation from the true value in the solution and provides constraint conditions during the convex optimization solution process, which is beneficial to improving the reconstruction accuracy. Experimental results show that this method can achieve a minimum MSE of 0.002 3 every 10 nm under the condition of ensuring high accuracy of MSE, ARE and RQE. The tunable spectrum reconstruction method based on spectrum achieves the effect of high-precision reconstruction of the target spectrum and achieves data dimensionality reduction. This method provides a new idea for the work direction in spectral reconstruction and has great application value in engineering.